**Q.12.
What is the Poisson distribution? **

**Ans.** Poisson distribution is a discrete probability
distribution. It is used in such cases where the value of his very large Since
in these cases binomail distribution does not give appropriate theoretical
frequencies, Poisson distribution is found very appropriate. It is worth
mentioning that poisson distribution is a limiting form of binomial
distribution as n moves towards infinity and p moves towards zero but np or
mean remains constant and finite. Poisson distribution is used to describe the
behaviour of rare events such as number of germs in one drop of pure water,
number of printing errors per page, number of telephone calls arriving per
minute at a telephone switch board, etc.

**Q.13. Write the four uses of Poisson
distribution. **

**Ans.** The four uses of Poisson distribution are:

1. In insurance problems to count the number of casualties.

2. In biology to count the number of bacteria.

3. In counting the number of defects per item in statistical quality control.

4. Number of accidents taking place per day on a busy road.

**Q.14.
Describe the meaning of normal distribution.**

**Ans.** Normal distribution is a continuous probability
distribution in which the relative frequenes of a continuous variable are
distributed according to normal probability law. In simple words, it is
symmetrical distribution in which the frequencies are distributed evenly about
the mean of distribution

**Q.15.
Describe the four main properties of normal distribution. **

**Ans.** The four main properties of normal distribution are: 1.
Bell shaped,

2. Continuous distribution,

3. Equality of central value,

4. Equal distance of quartiles from median.

**Q.16.
Give any three importance of theoretical frequency distribution. **

**Ans.** The three importance of theoretical frequency
distribution are as follows:

**1.
Forecasting:** Theoretical
frequency distribution provides base for prediction, projection and forecasting.

**2.
Substitute of Actual Data:** They can be
used as substitutes for actual distribution, when to obtain the later is costly
or cannot be obtained at all.

**3. Test of Sampling:** Theoretical frequency distributions serve as benchmarks against which to compare the actual frequency distributions and to find out whether the difference is significant or is merely due to fluctuations of sampling.

**Q.17.
What are the three main characteristics of binomial distribution? **

**Ans.** The three main characteristics of binomial distribution
are:

**1.
Theoretical Frequency Distribution:** Binomial
distribution is a theoretical frequency distribution based on Bernoulli theorem
of algebra.

**2.
Discrete Probability Distribution:** The binomial
distribution is a discrete probability distribution in which the number of
successes 0, 1, 2, 3,…,n are given in whole numbers and not in fractions.

**3.
Presentation by Line Graph:** The binomial
distribution can also be presented graphically by means of line graph, in which
the number of successes is taken on X-axis and the probability of success is
shown on Y-axis. For example, if a coin is tossed, then the probability of head
or tail will be 1/2. If the coin is tossed twice, the probability of getting
heads will be as follows: P (one head) = 2/4 = 1/2 and P(two heads) = 1/4

**4.
Main Parameters:** p and q are
two main parameters of binomial distribution and the entire distribution can be
obtained with the help of these parameters.

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